Alpha-Particle Stopping Cross Section in Solids from 400 keV to 2 MeV

Abstract

Stopping cross sections of $\ensuremath{\alpha}$ particles from 400 keV to 2 MeV have been measured to an accuracy of \ifmmode\pm\else\textpm\fi{}3.6 to \ifmmode\pm\else\textpm\fi{}4.9% in 17 elements (Be, C, Mg, Al, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Ge, Pd, Ag, In, and Sn). The experimental method consists of the elastic scattering of $\ensuremath{\alpha}$ particles from a thick Ta backing onto which a thin layer of target element has been evaporated. The energy loss of $\ensuremath{\alpha}$ particles in the target film is determined by the difference in energy between $\ensuremath{\alpha}$ particles scattered from clean Ta and $\ensuremath{\alpha}$ particles scattered from Ta after having gone through the thin layer of target element. The results are compared with measurements by Porat and Ramavataram and by Gobeli and with estimates by Whaling; the discrepancies range from 1 to 20%. Structure in and a decrease of the $\ensuremath{\alpha}$-particle stopping cross section ${\ensuremath{\epsilon}}_{\ensuremath{\alpha}}$ with stopping element atomic number ${Z}_{2}$ are noticed in the region ${Z}_{2}=22\ensuremath{-}29$. This dependence is not predicted by the Bethe-Bloch formalism valid at higher velocities, nor by the Firsov or the Lindhard formalism valid at lower velocities. The oscillatory structure of ${\ensuremath{\epsilon}}_{\ensuremath{\alpha}}$ on ${Z}_{2}$ is discussed qualitatively by comparing ${\ensuremath{\epsilon}}_{\ensuremath{\alpha}}({E}_{\ensuremath{\alpha}})$ versus ${Z}_{2}$ with a Hartree-Fock-Slater potential $\ensuremath{\varphi}(r)$ versus $Z$, with ${E}_{\ensuremath{\alpha}}$ related to the radius $r$ by a velocity comparison. An empirical formula for ${\ensuremath{\epsilon}}_{\ensuremath{\alpha}}={\ensuremath{\epsilon}}_{\ensuremath{\alpha}}({E}_{\ensuremath{\alpha}}, {Z}_{2})$ has been constructed from the present measurements.